That's what always surprised me about the whole concept of BRICS nations. Those countries have more interest in competing with each other to get access to other markets than to work/stick together in any way.
Access to markets isn't an exclusive asset. They don't compete over it, and mostly they can't compete over it, because they already have it.
NATO: Russia is a threat to both Europe and the US, lets band together to make sure we can fight them.
EU: Europe keeps fighting wars, lets make our economies more inter-dependent so that doesn't happen as much.
For NATO, I can see the happy vassals thing (and that's what the Belgian PM was referring to), but can you explain who is the overlord in the EU example?
(This is mostly satire, even if I think 2 of the 3 second things were and are great ideas).